[scottie_m]

It depends? If the satellites used chemical rockets to produce stationkeeping thrust then they’d be long gone, but if they used some exotic power source who knows? If they had a good AI and power, there is no real limit on how long they could stay in orbit. If they were using technology like ours they’d be gone, but a hypothetical civilization might use exotic materials and power sources that would stand the test of time.

For the moon thing, the above applies, but assuming that they were obliterated we’d have to get pretty lucky to detect their remains. They could also be totally intact because there would be essentially no weathering, they would never be buried by shifting regolith, and so on.

[ss2003]

Anything sitting on the surface of the Moon would must likely completely buried by regolith after roughly 2 million years. Every lunar day dust particles are launched up from the surface only to fall back down at night.

[gpm]

Where do you get 2 million from? I.e. why not 20k or 200m?

[eunoia]

How much stationkeeping does a geostationary satellite have to do to remain in orbit over a long time scale?

I would think not much?

[ianai]

I think none if positioned well enough.

[gpm]

Things like the moon will perturb it - orbits assume a 2-body system when we are strictly speaking in a (chaotic) n-body system.

Over millions of years that will add up, honestly I'm hoping someone else will do the math/research and figure out if they add up to enough that they wouldn't still be orbiting earth.

[ianai]

That’s my point though. The moon hasn’t degraded and crashed into the earth so it’s clearly possible for a satellite to orbit the earth indefinitely - for some suitable definition of indefinite.

[scottie_m]

The moon’s orbit is taking it further from Earth over time, it it’s very far away and very massive, as well as being influenced by the Sun. A satellite’s mass is almost negligible, and compared to the Earth-Moon distance it’s distance from Earth is too. A pebble hitting the moon also isn’t going to do much to change its course, while the same pebble will do a lot more to a satellite. The same is true of dust.

[stouset]

The moon has a ton of mass and—therefore—inertia. The chaotic effects of the system are still present, but require dramatically larger timescales to notice any kind of effect.

[gpm]

The moon's stability is a good point, but not conclusive. The moon's orbit isn't perturbed by it's own gravity. It's also much larger, so much more mass (radius cubed)/surface area (radius squared), so less affected by solar wind, micro meteor impacts, and the like.

[pxi]

But still, it's more likely we'd find evidence of a distant past civilisation on the moon than on earth right?